Recently many different techniques have been taken into consideration to try to overtake this problem. Galerkin projection has widely been employed to develop new reduction strategies capable of exploiting the information of just a few full order solutions for different parameter values in order to perform efficient, accurate and much cheaper solutions for a different selection of the parameter (for fluid flows applications, [1]}, [2]}, [3]}, [4]}, [5]} represents relevant works). Many different choices are possible to take advantage of the dynamical content contained into high fidelity solutions. The most used ones are the Proper Orthogonal Decomposition (POD) (see [6]}, [7]}, [8]}, [9]}, [10]}), the Proper Generalized Decomposition (PGD) (see [11]}, [12]}), the Dynamic Mode Decomposition (DMD) (see [13]}, [14]}) or the Greedy algorithm (see [15]}, [16]}).
